OK, looking at what we have in the source repository and how it all fits together...
Subversion: a storage system for the source of Emerald Editor, which allows us to revisit previous versions of the code and helps prevent edits being done by many people which would ultimately otherwise disintegrate EE.
wxWidgets: a toolkit responsible for building the graphical user interface. Basically, EE calls wxWidgets, wxWidgets calls whatever it appropriate for the operating system, be it Windows, Mac OS X, Linux or whatever. The result is that EE only has 1 set of code and this is applicable for each operating system.
Scintilla: a library which provides an "editing control", much like the editing section (only) of Crimson Editor. EE will use most of the features of Scintilla to do the actual editing. Scintilla itself also provides many of the features required for syntax highlighting, although we will have to rewrite the backend of that (Scintilla currently has its languages prebuilt into it, while we want to add customisable syntax files)
wxStEdit: rarely mentioned, but important to point out. Basically, wxStEdit is a functional text editor in its own right, using wxWidgets and Scintilla. Most of the EE code as it stands right now is a functional, buildable copy of wxStEdit. We are using this as a base since it already builds, is functional and we can remove and add features as we see fit. Within 3 days of the basic build being provided, the community was able to build what we have with minor work and alterations, on Windows, Linux and Mac OS X. This will become more important as time goes on if we hope to drive EE as the premier editing solution.
Everything else is done by MinGW/MSYS/MsysDTK (for Windows). Basically, EE is being written in C++ and those tools are part of what turns the code into a final usable program. Essentially we are using a package called GCC, the GNU Compiler Collection, which includes C and C++, but GCC is predominantly aimed at Linux/Unix (and Mac OS X) users.
The GCC tools, and "make" which binds it all together, are bundled up nicely into a single package for Windows, called MinGW (Minimalist GNU for Windows). However, some of the results of make and scripts that work with it don't always fit well into the Windows ideal, so a minimal system was put together, mirroring Linux/Unix-like behaviour on Windows - this is MSYS. Other packages which are useful but not critical to development are also available with MsysDTK, although this is a bonus rather than a dependence. You don't need MinGW, MSYS or MsysDTK to use EE, only to build new versions from the code we have.
The other tool which has been mentioned is bakefile. When building a large program, using hundreds of files of code (sometimes thousands), it is tedious to write a list of instructions to GCC on how to build it, including where to find libraries and resources, so all of these instructions are bundled up into a makefile, which is a set of instructions for "make" on how to build the program.
bakefile is a tool which helps construction of the makefile, and can simplify it in such a way that future makefiles don't rely on specific Windows, Linux, Mac OS X etc. behaviours in order to work.
I hope that's helped clear everything up - if not, please ask!